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Hello @bw1111 .
Your request is not related to Quick Featured Images but to WordPress.
Access to the “Featured Image” box is controlled by the WordPress capability upload_files. You have to make sure the role does have the upload_files permission. Please note, this includes access to the Media Library. The role can than upload any file.
As you can see here, role Author has the capability upload_files by default, contributor not.
Hope this helps.